Estimation of limited dependent variable models with dummy endogenous regressors: Simple strategies for empirical practice

Applied economists have long struggled with the question of how to accommodate binary endogenous regressors in models with binary and nonnegative outcomes. I argue here that much of the difficulty with limited dependent variables comes from a focus on structural parameters, such as index coefficients, instead of causal effects. Once the object of estimation is taken to be the causal effect of treatment, several simple strategies are available. These include conventional two-stags least squares, multiplicative models for conditional means, linear approximation of nonlinear causal models, models for distribution effects. and quantile regression with an endogenous binary regressor. The estimation strategies discussed in the article are illustrated by using multiple births to estimate the effect of childbearing on employment status and hours of work.